The system Zn1-xMnxFe2O4 (x = 0, 2, and 4%) was prepared by sol–gel chemical route at 80 °C. X-Ray powder diffraction Raman spectrum analysis were used to determine the preliminary phase of obtained samples. W–H SSP plots crystallite size micro-strain surface charge morphology samples studied using zeta potential scanning electron microscope analysis, respectively. optical bandgap suggested tha...

the rings considered in this article are  commutative  with identity which admit at least two  nonzero annihilating ideals. let $r$ be a ring. let $mathbb{a}(r)$ denote the set of all annihilating ideals of $r$ and let $mathbb{a}(r)^{*} = mathbb{a}(r)backslash {(0)}$. the annihilating-ideal graph of $r$, denoted by $mathbb{ag}(r)$  is an undirected simple graph whose vertex set is $mathbb{a}(r)...

In the p-th cyclotomic field Qpn , p a prime number, n ∈ N, the prime p is totally ramified and the only ideal above p is generated by ωn = ζpn − 1, with the primitive p-th root of unity ζpn = e 2πi pn . Moreover these numbers represent a norm coherent set, i.e. NQpn+1/Qpn(ωn+1) = ωn. It is the aim of this article to establish a similar result for the ray class field Kpn of conductor p over an ...

Let [Formula: see text] be a commutative ring with unity. The prime ideal sum graph of the is simple undirected whose vertex set nonzero proper ideals and two distinct vertices are adjacent if only text]. In this paper, we characterize all finite non-local rings genus

We give a description of the minimal primes of the ideal generated by the 2×2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m×m minors of an m×n generic matrix when the characteristic of the ground field is zero. A key intermediate result is the proof that the ideals which appear as minimal primes are, in fact, prime ideals. This ...

We establish a necessary condition for a commutative Banach algebra A so that there exists a homomorphism θ from A into another Banach algebra such that the prime radical of the continuity ideal of θ is not a finite intersection of prime ideals in A. We prove that the prime radical of the continuity ideal of an epimorphism from A onto another Banach algebra (or of a derivation from A into a Ban...

We give an elementary proof that for a ring homomorphism A → B satisfying the property that every ideal in A is contracted from B the following property holds: for every chain of prime ideals p0 ⊂ . . . ⊂ pr in A there exists a chain of prime ideals q0 ⊂ . . . ⊂ qr in B such that qi ∩ A = pi. Mathematical Subject Classification (1991): 13B24. Let A and B be commutative rings and let φ : A → B b...